Interior penalty finite element approximation of Navier-Stokes equations and application to free surface flows

In the present work, we investigate mathematical and numerical aspects of interior penalty finite element methods for free surface flows. We consider the incompressible Navier-Stokes equations with variable density and viscosity, combined with a front capturing model using the level set method. We formulate interior penalty finite element methods for both the Navier-Stokes equations and the level set advection equation. For the two-fluid Stokes equations, we propose and analyze an unfitted finite element scheme with interior penalty. Optimal a priori error estimates for the velocity and the pressure are proved in the energy norm. A preconditioning strategy with adaptive reuse of incomplete factorizations as preconditioners for Krylov subspace methods is introduced and applied for solving the linear systems. Different and complementary solutions for reducing the matrix assembly time and the memory consumption are proposed and tested, each of which is applicable in general in the context of either multiphase flow or interior penalty stabilization. As level set reinitialization method, we apply a combination of the interface local projection and a fast marching scheme. We provide for the latter a reformulation of the distance computation algorithm on unstructured simplicial meshes in any spatial dimension, allowing for both an efficient implementation and geometric insight. We present and discuss numerical solutions of reference problems for the one-fluid Navier-Stokes equations and for the level set advection problem. Solutions of benchmark problems in two and three dimensions involving one or two fluids are then approximated, and the results are compared to literature values. Finally, we describe software design techniques and abstractions for the efficient and general implementation of the applied methods

What is the Minimum to Trust AI?—A Requirement Analysis for (Generative) AI-based Texts

The generative Artificial Intelligence (genAI) innovation enables new potentials for end-users, affecting youth and the inexperienced. Nevertheless, as an innovative technology, genAI risks generating misinformation that is not recognizable as such. The extraordinary AI outputs can result in increased trustworthiness. An end-user assessment system is necessary to expose the unfounded reliance on erroneous responses. This paper identifies requirements for an assessment system to prevent end-users from overestimating trust in generated texts. Thus we conducted requirements engineering based on a literature review and two international surveys. The results confirmed the requirements which enable human protection, human support, and content veracity in dealing with genAI. Overestimated trust is rooted in miscalibration; clarity about genAI and its provider is essential to solving this phenomenon, and there is a demand for human verifications. Consequently, our findings provide evidence for the significance of future IS research on human-centered genAI trust solutions

Anforderungen an Endkunden-Demand-Response-Informationssysteme

Demand Response-Initiativen bieten eine große Chance, einen nachhaltigen Beitrag zur Erreichung umweltrelevanter Ziele zu leisten. Die Vorteile dieser kundenseitig ansetzenden, lastverschiebenden und lastreduzierenden Maßnahmen können heute jedoch auf Grund zahlreicher Problemstellungen noch nicht internalisiert werden. Vor dem Hintergrund der steigenden Anzahl vernetzter Verbraucher in Haushalten (z.B. durch Smart Home-Technologie) bieten sich neue Möglichkeiten zur Anbindung privater Haushalte an Demand Response-Programme. Eine Integration der Energie-Nachfrager erfolgt bisher allerdings hauptsächlich bei gewerblichen Kunden. Die vorliegende Literaturanalyse untersucht daher Anforderungen an die Entwicklung eines endnutzerseitig installierbaren Informationssystems zur Integration vernetzter Verbraucher an Demand Response-Programme und analysiert dabei insbesondere die Rolle des Datenaustausches

The Road to Success: Recommendations for the Design of Successful Business Process Modeling Initiatives

Process modeling is among the most important activities in the business process management lifecycle and enables enterprises to improve communication, coordination, and knowledge management. However, enterprises frequently face challenges when introducing process modeling to their organization. These range from a lack of strategic alignment to insufficient stakeholder participation leading to pitfalls, such as project failure or outcomes that do not meet predefined expectations. Hence, we present findings from eight successful process modeling initiatives and consolidate them to a decision-support framework. The contribution of this research is twofold. First, our study suggests that the success of process modeling depends on contextual parameters, including top management involvement, tool support, and employee education. Second, the design of process modeling initiatives fundamentally changes with organizational objectives. Based on a clear set of goals, enterprises can choose from at least three success strategies that require a unique configuration and structure

Simulation of impaction filtration of aerosol droplets in porous media

We report on the development of a method to simulate from first principles the particle filtration efficiency of filters that are composed of structured porous media. We assume that the ratio of particle density to the fluid density is high. We concentrate on the motion of the particles in a laminar flow and quantify the role of inertial effects on the filtration of an ensemble of particles. We adopt the Euler-Lagrange approach, distinguishing a flow field in which the motion of a large number of discrete particles is simulated. We associate filtration with the deterministic collision of inertial particles with solid elements of the structured porous medium. To underpin the physical `consistency' of deterministic particle filtration, we investigate to what extent the particle tracking algorithm ensures that mass-less test-particles will not be captured by the structured porous filter at all. This element of the algorithm is essential in order to distinguish physical filtration by inertial effects from unwanted numerical filtration, due to the finite spatial resolution of the gas flow. We consider filtration of particles whose motion is governed by Stokes drag and determine the filtration efficiency in a range of Stokes relaxation times. An exponential decay of the number of particles with time is observed

Decrease in the expression of the type 1 PTH/PTHrP receptor (PTH1R) on chondrocytes in animals with osteoarthritis

<p>Abstract</p> <p>Background</p> <p>To evaluate the expression of the type 1 PTH/PTHrP receptor (PTH1R) on chondrocytes from hyaline cartilage over the course of osteoarthritis (OA).</p> <p>Methods</p> <p>In 12 NZW rabbits, the anterior cruciate ligament (ACL) was resected to create anterior instability of the knee. In 12 control rabbits, only a sham operation, without resection of the ACL, was performed. Four animals from each group were killed at 3, 6, and 12 weeks. After opening the knee joint, OA was macroscopically graded and hyaline cartilage of the load-bearing area was evaluated histologically according to the Mankin scale and by immunostaining for PTH1R.</p> <p>Results</p> <p>There was a positive linear correlation between the time after surgery and the macroscopic and histologic OA scores. The scores in the control group were constant over the time course. Immunostaining showed significantly less expression of PTH1R in the experimental compared to the control group after 6 (P < 0.05) and 12 weeks (P < 0.01). In the experimental group, a negative linear correlation between PTH1R expression and macroscopic and histologic grades was found.</p> <p>Conclusions</p> <p>The results show an in vivo decrease in the expression of PTH1R on chondrocytes over the time course of OA. Further studies are needed to evaluate whether new treatment approaches could evolve from this knowledge.</p

TKA following high tibial osteotomy versus primary TKA - a matched pair analysis

<p>Abstract</p> <p>Background</p> <p>High tibial osteotomy (HTO) is a well established technique for the treatment of medial osteoarthritis of the knee with varus malalignment. Results of total knee arthroplasty (TKA) after previous HTO are still discussed controversially. The aim of this study was to elucidate the clinical and radiological results as well as perioperative data of prior HTO on TKA.</p> <p>Methods</p> <p>Forty-one TKA after HTO were compared to 41 primary TKA at minimum of six years follow-up. Patients were matched according to age, gender, follow-up, etiology, and prosthetic design. Surgical data and complications were evaluated. Clinical outcome was assessed using a number of clinical scores and the visual analogue scale (VAS) for pain. X-rays were evaluated by the method of the American Knee Society. The patellar position was measured by the Insall-Salvati ratio.</p> <p>Results</p> <p>There was no significant difference in mean operation time (p = 0.47) and complication rate (p = 0.08). The Knee Score of the KSS (p = 0.0007) and the ROM (p = 0.006 for extension and p = 0.004 for flexion, respectively) were significantly better in the control group. Mid-term results of the VAS, WOMAC, Lequesne, UCLA, Feller's Patellar Score and SF-36 showed no significant difference. Femoral and tibial component alignment were similar in both groups. One tibial component showed suspect radiolucencies in the HTO group. The Insall-Salvati ratio showed three patients with patella alta and one patient with patella baja in the HTO group. At latest follow-up all implants were still in place.</p> <p>Conclusions</p> <p>Evaluating the clinical and radiological outcome, significant differences were only detected for range of motion and the Knee Score of the KSS. The present study suggests that the results of TKA with and without prior HTO are mainly identical. Although patients with a previous HTO had more complications, no statistically significant differences were noted with this group size.</p

A dispersion-engineered multi-pass cell for single-stage post compression of an Ytterbium laser

Post-compression methods for ultrafast laser pulses typically face challenging limitations including saturation effects and temporal pulse break-up when large compression factors and broad bandwidths are targeted. To overcome these limitations, we exploit direct dispersion control in a gas-filled multi-pass cell, enabling for the first time single-stage post-compression of 150 fs pulses and up to 250 uJ pulse energy from an Ytterbium (Yb) fiber laser down to sub-20 fs. Dispersion-engineered dielectric cavity mirrors are used to achieve nonlinear spectral broadening dominated by self-phase-modulation over large compression factors and bandwidths at 98% throughput. Our method opens a route towards single-stage post-compression of Yb lasers into the few-cycle regime

Dispersion-engineered multi-pass cell for single-stage post-compression of an ytterbium laser

Post-compression methods for ultrafast laser pulses typically face challenging limitations, including saturation effects and temporal pulse breakup, when large compression factors and broad bandwidths are targeted. To overcome these limitations, we exploit direct dispersion control in a gas-filled multi-pass cell, enabling, for the first time to the best of our knowledge, single-stage post-compression of 150 fs pulses and up to 250 µJ pulse energy from an ytterbium (Yb) fiber laser down to sub-20 fs. Dispersion-engineered dielectric cavity mirrors are used to achieve nonlinear spectral broadening dominated by self-phase modulation over large compression factors and bandwidths at 98% throughput. Our method opens a route toward single-stage post-compression of Yb lasers into the few-cycle regime